It must have been a risk as an author, to try to combine two different and well-established genres. There has been a tradition on Napoleonic naval series: Marryat, Forester, O'Brian,... with a focus on historical action, generally appealing to conservative men. Then there are fantasy novels with dragons, including The Hobbit, McCaffrey, Le Guin, etc etc. Not, one might think, an easy combination to put together.
However, Novik succeeds, and in doing so reinvigorates the Napoleonic naval genre. There is, after all, only a limited number of plot turns that can be extracted from the historical record, and Patrick O'Brian has already found them. Novik asks, what would have happened if, and so lets us understand Georgian society better.
The series then is an alternative history, in which dragons exist and are used to fight wars alongside ships of the line, hussars and cannon. The first book starts in 1805 when Nelson and his fleet (and attached dragons) are blockading France. Wellesley, the Jiaqing Emperor, and Napoleon appear in later books (with dragons). The first book is fairly close to history, but later books diverge more.
Much of the interest is in conflicts between the characters' upbringing and the unexpected challenges brought out by the dragon wars. This is particularly the case for the main character, Captain Lawrence, who is the captain of the dragon Temeraire. Lawrence starts the series as a naval captain, the son of an earl, and very much a traditional English aristocrat. In the first book, he first needs to overcome his prejudices against the dragon corps when he is forced by circumstances to transfer; over the following books he reassesses his instinctive views on slavery, patriotism, military duty, and marriage.
This book was titled Temeraire in the United Kingdom edition, but this was evidently to obscure a reference for the Americans. It is the first of the Temeraire series.